A Crash Course in Predicate Logic

Logic for Programmers is a book that aims to introduce programmers to the concepts and syntax of formal logic. The author has converted the second chapter of the book into a blog post to provide a free resource for programmers. The chapter covers fundamental concepts such as predicates, implication operators, sets, and set quantifiers. Many programmers may already be familiar with these concepts from their programming experience.

A predicate is essentially a function that returns a Boolean value. Programmers often write predicates without realizing it, as they frequently write functions that return true or false based on certain conditions. For example, a predicate like RAMAtLeast might be used to check if a computer has enough RAM. Although predicates are a mathematical concept, they can be applied in programming to define abstract concepts that may be difficult or impossible to compute.

To distinguish between abstract and concrete predicates, the author suggests using backticks for abstract predicates and TitleCase for their bodies. Concrete predicates, on the other hand, can be computed and will always be written in snake_case. The author also suggests using TitleCase for predicates and snake_case for functions to maintain consistency.

Predicates can be combined using Boolean operators such as AND, OR, and NOT. In programming, these are often represented using symbols like &&, ||, and !. The author introduces the four Boolean operators, including the fourth operator =, which may have different meanings in different contexts.

By using formal logic, programmers can express complex requirements more clearly and unambiguously. Formal logic can help eliminate ambiguity in requirements and make them easier to understand and implement. The chapter also covers truth tables, a useful tool for analyzing the behavior of predicates and making decisions based on logical expressions.